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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

What is the smallest integer x for:

equation

to be a perfect square?

Factor the number into primes:

equation

equation

equation

equation

equation

For a number to be a perfect square, all its prime factors have to have an even exponent.

The number we have already has an even number of factors of 2.

We need an extra number of factors to bring the other prime factors to the smallest even power. N has to look like this:

equation

Therefore, the smallest x has to be:

equation

equation